Water raised by counterweights and finding its level

Water rising above its level and the driving weight

Water that rises into the air above its level never weighs as much as the weight that drives it up. The weight of water leaping through a pipe bears the same proportion to the driving water as the bore of the pipe bears to the tank from which it issues. The pressing weights may be thicker, thinner, or equal to the tank, and of matter heavier, lighter, or equal to water, as lead, wood, and water itself.

Stone and water counterweights pressing the tanks

Four tanks marked stone, stone, water, water illustrate that two counterweights of equal weight upon equal instruments have equal power. If a water counterweight equals the tank's bore in width, the part that acts on the leaping water equals the pipe's bore; but if it were ten times wider than the tank, the water would rise ten times higher than the counterweight's own surface.

A descending weight cannot raise an equal weight

It is impossible for a descending weight to raise a weight equal to itself to the height from which it fell, for any length of time; so let those be silent who hope with a counterweight to raise water heavier than the counterweight. Raising 1,000 pounds by one braccio, the descent carries only about 100 pounds of water nine braccia and no more. As the pressing weight descends, the mass of water that rises diminishes by as much.

Communicating vessels settle to one level

In pipes a b open at the top, the enclosed air touches the water at the same level as the outside air, because it joins the common air. But air shut in pipe n, cut off from the common air, meets its water at a different level. By the propositions cited, waters b and a, d and c, and m and n all stand level with one another.

Water level and the centre of the world

Every level begins on the perpendicular running to the centre of the world, meeting the central line at a right angle, so the level line runs straight and grows ever more distant from the centre as it lengthens. Thus water that has descended cannot of itself rise again to its level height. In the quarter of the world, water called flat rises above its level 3,500 miles in 5,600 miles of sea line.

The 3-4-5 right triangle and squares on its sides

At the top a right triangle carries the side measures 4, 3 and 5. Squares built on its sides are labelled 16 on 4, 9 on 3, and 25 on 5, so that the two smaller squares together equal the largest. This is the Pythagorean relation set out numerically.

Presso il margine superiore. Triangolo colle misure dei lati:

Quadrati costruiti sui lati d'un ortogonio, con:

Colonna destra.

Segue sotto i disegni:

Figure di quattro bottini, con:

Lungo il margine superiore dal centro a sinistra:

Colonna centrale. Settore di una sezione della terra coperta dal mare, con:

Due vasi con tubi aperti o chiusi immersi in acqua, con:

Due vasi comunicanti, con:

Figura analoga, con:

Vasi comunicanti, con:

Colonna sinistra.

Sezione di un quarto della terra, con:

Near the upper margin. Triangle with the measures of its sides:

Squares built on the sides of a right triangle, with:

Right column.

Continuing below the drawings:

Figures of four tanks, with:

Along the upper margin, from the centre to the left:

Central column. Sector of a section of the earth covered by the sea, with:

Two vessels with open or closed tubes immersed in water, with:

Two communicating vessels, with:

Analogous figure, with:

Communicating vessels, with:

Left column.

Section of a quarter of the earth, with: